1. Field of the Invention
The present invention relates to a charge trajectory calculating method, system, and program.
2. Background Art
Scanning electron microscopes (SEMs) enable observation of extremely small objects. The importance of the SEM technology is growing with the development of the nanotechnology. In the semiconductor industry, the SEM technology has been used for inspection and length measurement.
Recently, in the semiconductor industry, requirements on the inspection and length measurement have become stricter as semiconductor design rules become finer. According to the strictest specification, precision in the inspection and length measurement has to be on the order of sub-nanometer. Further, in addition to high precision in the inspection and length measurement, high stability in the inspection and length measurement is also required. In order to meet the requirements, it is attempted to raise resolution and stability of an SEM apparatus to improve the hardware of an SEM, and attempted to develop such an inspection method and length measurement method as improving reproducibility to improve the software of an SEM.
When using an SEM, SEM conditions such as accelerating voltage, sample current, and bias voltage have to be optimized. Whether the SEM conditions can be appropriately optimized or not is largely dependent on the skill of an operator. When using the SEM, the operator places a measuring sample in the SEM, and optimizes the SEM conditions by varying the SEM conditions by trial and error. Optimization of the SEM conditions often takes a long time and may take several days in some cases. This has a significant effect on the turn around time (TAT) of a semiconductor manufacturing process. In the semiconductor manufacturing process, reduction of the TAT is imperative because the TAT has a significant effect on the cost. It is undesirable for the semiconductor manufacturing process to take a long time to optimize the SEM conditions.
In recent years, SEM simulations using the Monte Carlo method have become popular. In the past, a Monte Carlo calculation required an enormously long calculation time. However, the development of the information processing technology in recent years has enabled the Monte Carlo calculation to be performed in a relatively short time. According to an SEM simulation, the SEM conditions can be optimized without an actual measuring sample before the inspection or length measurement (see JP-A 2002-75818 (KOKAI)).
A typical flow of the SEM simulation will be described hereinafter.
First, a simulation region which corresponds to the existence region of a measuring object, is provided. In this step, the number of calculation meshes in the simulation region is determined, and the calculation meshes are provided in the simulation region. In this example, the number of calculation meshes in the simulation region is 9×9, i.e., 81.
Next, it is assumed that one of the meshes is irradiated with an electron beam. Then, trajectories of scattered charges, the charge distribution, and the potential distribution in the simulation region are calculated. Such a calculation is repeated 81 times on the assumption that the 81 meshes are scanned (i.e., successively irradiated) with the electron beam. The calculation may be performed by the two or more meshes. For example, if the calculation is performed by the three meshes, the calculation is repeated 27 times.
The calculation of the potential distribution from the charge distribution is performed using the Poisson equation. For the calculation, the finite element method is often used. When calculating the potential distribution, charge movement has to be appropriately taken into account. Further, to raise precision of the calculation of the potential distribution, fine meshes have to be provided. However, it is difficult to meet these requirements without increasing load on a computer and elongating time for calculating the potential distribution.
For this reason, it is attempted to perform an SEM simulation using a cluster PC, which includes a plurality of PCs. The cluster PC includes, for example, a master node and a plurality of cluster nodes. The master node generates a random number, distributes charge scattering calculations and charge distribution calculations among the cluster nodes, collects charge information from the cluster nodes, and performs potential distribution calculations. The computational capability of the cluster PC increases as the number of the cluster nodes increases.
Exchanges of data between the master node and the cluster nodes are performed via a network, such as a LAN. The time required for the data communication increases in proportion to the number of the cluster nodes. As the number of the cluster nodes increases, the proportion of the data communication time in the entire calculation time becomes considerable.
As described above, the SEM simulation has a large technical problem regarding how to reduce the calculation time.